Small-scale effects of thermal inflation on halo abundance at high-$z$, galaxy substructure abundance, and 21-cm power spectrum

We study the impact of thermal inflation on the formation of cosmological structures and present astrophysical observables which can be used to constrain and possibly probe the thermal inflation scenario. These are dark matter halo abundance at high redshifts, satellite galaxy abundance in the Milky Way, and fluctuation in the 21-cm radiation background before the epoch of reionization. The thermal inflation scenario leaves a characteristic signature on the matter power spectrum by boosting the amplitude at a specific wave number determined by the number of e-foldings during thermal inflation ($N_{bc}$), and strongly suppressing the amplitude for modes at smaller scales. For a reasonable range of parameter space, one of the consequences is the suppression of minihalo formation at high redshifts and that of satellite galaxies in the Milky Way. While this effect is substantial, it is degenerate with other cosmological or astrophysical effects. The power spectrum of the 21-cm background probes this impact more directly, and its observation may be the best way to constrain the thermal inflation scenario due to the characteristic signature in the power spectrum. The Square Kilometre Array (SKA) in phase 1 (SKA1) has sensitivity large enough to achieve this goal for models with $N_{bc}\gtrsim 26$ if a 10000-hr observation is performed. The final phase SKA, with anticipated sensitivity about an order of magnitude higher, seems more promising and will cover a wider parameter space.

Figure 1

Characteristic scales of cosmology with thermal inflation. There are five characteristic scales, $k_a$, $k_b$, $k_c$, $k_d$ and $k_e$ corresponding to the comoving scale of the horizon at each of the era boundaries. $k_b$ is the largest, and hence the most observable scale.

Figure 2

Transfer function induced by thermal inflation, ${\mathcal{T}}_{\mathrm{TI}}^2(k)$, as a function of $k/k_b$ [21].

Figure 3

The allowed range of primordial power spectra ${\mathcal{P}}_{\mathcal{R}}^{\mathrm{pri}}$ in thermal inflation scenario with $1{\mathrm{Mpc}}^{-1}\le k_b\le {10}^2{\mathrm{Mpc}}^{-1}$, normalized with the amplitude at the pivot scale $k_{*}=0.05{\mathrm{Mpc}}^{-1}$. Black dash: Standard $\mathrm{\Lambda }\mathrm{CDM}$ scenario without spectral index running.

Figure 4

Evolution of matter power spectra ${\mathrm{\Delta }}^2(k)\equiv k^3{P}_m(k)/2{\pi }^2$ for thermal inflation and warm dark matter scenarios from $z=20$ to 0. Solid lines: thermal inflation scenarios with $k_b=1{\mathrm{Mpc}}^{-1}$ (red), $3{\mathrm{Mpc}}^{-1}$ (yellow), $10{\mathrm{Mpc}}^{-1}$ (green), $30{\mathrm{Mpc}}^{-1}$ (cyan), and $100{\mathrm{Mpc}}^{-1}$ (blue). The change of power spectra from the choice of different ${\mathcal{N}}_{*}$ is negligible. Dashed lines: WDM scenarios with $m_{\mathrm{FD}}=1\mathrm{keV}$ (brown) and 2 keV (magenta). Black dash: standard $\mathrm{\Lambda }\mathrm{CDM}$ scenario.

Figure 5

The standard deviation of the matter density field smoothed by a window function with length scale, $R(M)\equiv (3M/4\pi {\overline{\rho }}_m{)}^{1/3}$, for a given mass scale $M$, for thermal inflation and WDM scenarios. Color codes and line styles are the same as Fig. 4.

Figure 6

Evolution of global halo mass functions $n(>M)$ for thermal inflation and WDM scenarios from $z=20$ to 0, calculated by the various mass function models (symbols). Lines: the mass function described in [54]. Color codes and line styles are the same as Fig. 4 and Fig. 5.

Figure 7

The cumulative number of satellite galaxies of simulated Milky Way-size halos, $N(>V_{\mathrm{c}})$, for thermal inflation scenarios (left panel) with $k_b=1{\mathrm{Mpc}}^{-1}$ (red), $3{\mathrm{Mpc}}^{-1}$ (yellow), WDM scenarios (right panel) with $m_{\mathrm{FD}}=1\mathrm{keV}$ (brown), 2 keV (magenta), and the standard $\mathrm{\Lambda }\mathrm{CDM}$ scenario (black) at $z=0$. $V_{\text{global}}$ and $V_c$ are the circular velocities of the Milky Way and one of its satellite galaxies indicating its mass ($V_c\propto M^{1/3}$). Line and error bar show the median and $1\sigma$ deviation. Symbols: results from previous studies on satellite abundance in WDM scenarios, by adopting $V_{\text{global}}=218\mathrm{km}/\mathrm{s}$ [68].

Figure 8

The 21-cm power spectra ${\mathrm{\Delta }}_{21}^2(k)\equiv k^3{P}_{\delta T_b\delta T_b}(k)/2{\pi }^2$ of thermal inflation and WDM scenarios (colors) just before the epoch of reionization. Shaded regions: the power spectra above the thermal noise from the modified SKA configuration with $100{\mathrm{deg}}^2$ sky coverage. Exposure times are $10^3$ (cyan), $10^4$ (orange), and $10^5$ (gray) hours in SKA1-LOW, and $10^2$ (cyan), $10^3$ (orange), and $10^4$ (gray) hours in SKA2-LOW [81]. The upturn of the noise power spectrum at $k\sim 0.1h{\mathrm{Mpc}}^{-1}$ [81] is not shown in this plot, because our main interest lies at $k\gtrsim 1h{\mathrm{Mpc}}^{-1}$.